Question

1. 54, 45
2. 25, 55
3. 68, 34
4. 54, 27
5. 55, 75
6. 66yx, 30x²y
7. 60y, 56x²
8. 36xy³, 24y²
9. 18y², 54y²
10. 80x³, 30yx²
11. 105x, 30yx, 75x
12. 140n, 140m², 80m²

Explanation:

Let's solve problem 7: finding the greatest common divisor (GCD) of 54 and 45.

Step 1: Prime Factorization

Find the prime factors of 54 and 45.

• Prime factors of 54: \( 54 = 2 \times 3 \times 3 \times 3 \)
• Prime factors of 45: \( 45 = 3 \times 3 \times 5 \)

Step 2: Identify Common Factors

The common prime factors of 54 and 45 are \( 3 \times 3 \).

Step 3: Calculate GCD

Multiply the common prime factors: \( 3 \times 3 = 9 \)

Answer:

The GCD of 54 and 45 is 9.